Shading and Illumination

OpenGL Shading

Without Shading With Shading

Physics

ω

Bidirectional Reflectance Distribution Function (BRDF)

fr (ω i,ω)=dL(ω)

L(ω i)cosθidω i

=dL(ω)

L(ω i)(−ω i ⋅n)dω i

θi

n: Surface normalL: Radiance (“intensity along a ray”)

Light Events

Reflection Refraction Scattering

Bidirectional Reflectance Distribution Function (BRDF)

Bidirectional transmittanceDistribution Function (BTDF) Scattering Function

Bidirectional Scattering Distribution Function (BSDF)

Rendering Equation• Given any point x in a large environment, let L(x, ω)

be the radiance along a ray, we have:

L(x,ω)=Le(x,ω)+ fr(Ω∫ x,ω i,ω)L(x,ω i)(−ω i ⋅n)dω i

fr (ω i,ω)=dL(ω)

L(ω i)(−ω i ⋅n)dω i

ω

θi

Le: Emitted intensity (light source)Ω: A hemisphere over x

Light Transport

• The rendering equation describes a light transport problem:

• Each point has an integral equation.

• Light can be reflected multiple times, so those integral equations are highly related.

• Solution: global illumination.

• Methods: ray tracing, radiosity.

Example: Caustics

Example: Color Bleeding

OpenGL Illumination

• Unfortunately, OpenGL doesn’t support global illumination.

• Instead, it only considers local illumination: light can only be reflected once.

• Even for local illumination, OpenGL is not physically based. It only provides an approximation.

• To accurately get multiple reflections, you need to better rendering algorithms.

• You can approximate some global illumination effects using GPU programmable shaders.

OpenGL Illumination

• Light sources

• Surface material properties

• Surface normal

• Incoming (light) and outgoing (eye) directions

Point Light Source

GLfloat light_position[] = {1.0, 1.0, 1.0}; glLightfv(GL_LIGHT0, GL_POSITION, light_position);

Directional Light Source

GLfloat light_position[] = {1.0, 1.0, 1.0, 0.0}; glLightfv(GL_LIGHT0, GL_POSITION, light_position);

Spot Light Source

GLfloat light_position[] = {1.0, 1.0, 1.0}; glLightfv(GL_LIGHT0, GL_POSITION, light_position);Glfloat spot_position[] = {1.0, 1.0, 1.0}; glLightfv(GL_LIGHT0, GL_SPOT_DIRECTION, spot_position);Glfloat EXPONENT=10;glLightfv(GL_LIGHT0, GL_SPOT_EXPONENT, EXPONENT);Glfloat cutoff=30;glLightfv(GL_LIGHT0, GL_SPOT_CUTOFF, cutoff);

• OpenGL separates surface reflection into three components:

• Therefore, you should define three light intensities. Each of them contributes to a reflection component:• Ambient • Diffuse• Specular

OpenGL Light Intensity

Ambient Diffuse Specular Total

OpenGL Light Source

//To specify the light position and intensityGlfloat LightPosition []={100, 0.0, 100};Glfloat LightAmbient []={0.2, 0.2, 0.2};Glfloat LightDiffuse []={1.0, 1.0, 1.0};Glfloat LightSpecular []={0.4, 0.4, 0.4};

glLightfv(GL_LIGHT1, GL_POSITION, LightPosition);glLightfv(GL_LIGHT1, GL_AMBIENT, LightAmbient);glLightfv(GL_LIGHT1, GL_DIFFUSE, LightDiffuse);glLightfv(GL_LIGHT1, GL_SPECULAR, LightSpecular);

OpenGL Light Source• For a point light source, the light intensity drops when the

light moves away from the source. So OpenGL multiplies the intensity with an attenuation factor:

attenuation =1

Aconstant + dAlinear + d2Aθuadratic

glLightf(GL_LIGHT0, GL_CONSTANT_ATTENUATION, 2.0); glLightf(GL_LIGHT0, GL_LINEAR_ATTENUATION, 1.0); glLightf(GL_LIGHT0, GL_QUADRATIC_ATTENUATION, 0.5);

Default Values

No ambient

Unit diffuse

Unit specular

Directional light along z

No attenuation

No spot light

Multiple Light Sources

//Specify the position and properties for GL_LIGHT0glEnable(GL_LIGHT0);//Specify the position and properties for GL_LIGHT1glEnable(GL_LIGHT1);//Create other light sources here.glEnable(GL_LIGHTING);

//You can turn on and off lights like this:glDisable(GL_LIGHT0);glEnable(GL_LIGHT0);glDisable(GL_LIGHTING);glEnable(GL_LIGHTING);

OpenGL Light Source

• The light source is subject to the MODELVIEW matrix as well.

• You can create the light source in the eye space, so it always attached to the camera.

• You can create the light source after camera motion, so it is fixed in the world space.

• You can even apply extra transformation/animation to light source.

• OpenGL separates surface reflection into three components:

• Therefore, you should define three material properties. Each of them contributes to a reflection component:• Ambient • Diffuse• Specular

OpenGL Material

Ambient Diffuse Specular Total

Ambient Reflection

Lambient =Iam bient ⋅Kam bient

Ambient Radiance(Pixel Intensity)

Ambient Light

Ambient Surface Material Coefficient

• The object will have a uniform color.

• It looks similar to the result without lighting.

• The color is not directly assigned. It’s controlled by the light source and surface reflection coefficient.

Diffuse Reflection• Diffuse reflection assumes that the light is

equally reflected in every direction.

• In other words, if the light source and the object has fixed positions in the world space, the camera motion doesn’t affect the appearance of the object.

• The reflection only depends on the incoming direction. It is independent of the outgoing (viewing) direction.

• Real objects with only a diffuse reflection property are called: Lambertian Surfaces, for example, clay.

Diffuse Reflection

• Lambert’s law says that the outgoing radiance depends on the cosine of the incident angle.

• Because the irradiance (photons per unit surface area) becomes smaller (as in the rendering function before).

dA

dA

dA

dA/cosθi

θi

Diffuse Reflection

θi

Ldiffuse =Idiffuse ⋅Kdiffuse cosθi

Diffuse Radiance

Diffuse Light

Diffuse Surface Material Coefficient

Brighter Darker

An ExampleKdiffuse

Kambient

Specular Reflection

• Some materials, such as plastic and metal, can have shiny highlight spots.

• This is due to a glossy mirror-like reflection.

• Materials have different shininess/glossiness.

Specular Reflection

• For a mirror, the light is reflected into a single direction.

• Specular reflection assumes that the glossy surface is not even, so the light is reflected into a small cone.

• If your viewing direction is close to the mirror direction, you receive high radiance.

θi θi

N

θiϕ

N

Specular Reflection

θi ϕ

NLV

R

• Given L, N and V, we first calculate the mirror reflection direction:

• Then we have:

R = 2(L⋅N)N- L

Lspecular =Ispecular⋅Kspecularcosnφ

ϕ is the angle between V and R.cosφ =V ⋅R

n indicates surface shininess.

An ExampleKspecular

Shininess n

Total Reflection• Illumination from a single light source i:

• Illumination from multiple light source:

Lspecular =Ispecular⋅Kspecularcosnφ

Lambient =Iam bient ⋅Kam bient

Ldiffuse =Idiffuse ⋅Kdiffuse cosθi

Ltotali =Lam bient

i + Ldiffusei + Lspecular

i

Ltotal =Lglobalam ibient + Ltotal0 + Ltotal

1 + Ltotal2 +L

OpenGL Material

• OpenGL defines material properties like this:

• Face: GL_FRONT, GL_BACK, or GL_FRONT_AND_BACK• Property: GL_AMBIENT, GL_DIFFUSE, …• Value: A vector array

glMaterialfv("face”, "property”, “value”)

For Example

Glfloat mat_amb_diff[]={1.0, 0.5, 0.8, 10.0};Glfloat mat_specular[]={1.0, 1.0, 1.0, 1.0};Glfloat shiniess []={5.0};glMaterialfv(GL_FRONT, GL_AMBIENT_AND_DIFFUSE, mat_amb_diff);glMaterialfv(GL_FRONT, GL_SPECULAR, mat_specular);glMaterialfv(GL_FRONT, GL_SHININESS, shininess);

• Specular highlights are usually in the light source’s color.• Ambient and diffuse can be defined together or separately.• If you don’t mind dark shadow, just ignore ambient.• Shininess is from 0 (dull) to 128 (shiny).

Light Model

• Enable two-sided lighting• Property=GL_LIGHT_MODEL_TWO_SIDE• If value=0, only GL_FRONT is rendered; • If value=1, both GL_FRONT and GL_BACK are rendered

• Global ambient color• Property=GL_LIGHT_MODEL_AMBIENT• Value is a color array

• And more…

glLightModelfv(property, value);

Surface Normal• Normals are used in calculating reflection. Normals are also

used to decide the surface front and back side.

(x, y, z)

It’s normal isnormalized(x, y, z)

V0

V1

V2

E10=V1-V0

E20=V2-V0

N =E10× E20

E10× E20

Surface Normal

for(int i=0; i<t_number; i++){

glNormal3f(…);glBegin(GL_TRIANGLES);glVertex3f(…);glVertex3f(…);glVertex3f(…);glEnd();

}

• We can define a triangle normal for the whole triangle. The result is a surface made of triangles.

Surface Normal

for(int i=0; i<t_number; i++){

glBegin(GL_TRIANGLES);glNormal3f(…); //XN0glVertex3f(…); //X0glNormal3f(…); //XN1glVertex3f(…); //X1glNormal3f(…); //XN2glVertex3f(…); //X2glEnd();

}

• But the mesh represents a smooth surface. We define a normal for each vertex, by taking the normalized average of its adjacent triangle normals.

Lighting and Shading

Intersection Test

Given a 2D Pixel Location

Selection Ray

• Each pixel corresponds to a visible 3D point.• We need to calculate the pixel intensity for that 3D point,

based on the reflection model.

Inverse Projection

A 3D point on a polygon

Reflection Calculation

Ray Tracing

Rasterization

Given a 3D polygon

A 2D polygon

Projection

A number of pixels

The Graphics Pipeline

Lighting and Shading• OpenGL calculates reflection at each vertex.

Rasterization

Given a 3D primitive

A 2D polygon, with 3D info

Projection

Pixels with 3D info

OpenGL + GPU (Phong)

Fragment Shader

Pixels with intensities

Raserization

Given a 3D polygon

A 2D polygon, with intensity info

Projection

Pixels with intensitiesOpenGL

Lighting

A 3D polygon, with intensity info

Shading

Interpolation/Raserization

Given a 3D polygon

A 2D polygon, with info

Projection

Pixels with intensities

Lighting

A 3D polygon, with info

• Now given a 2D polygon with the value on each vertex, how to interpolate the value for each pixel?• Flat shading• Gouraud Shading*• Phong Shading*

*: Both were proposed by researchers at the University of Utah in 1970s.

Flat Shading• Flat shading uses one vertex’s intensity value for the whole

polygon. glShadeModel(GL_FLAT)

Vertex Normal + Flat Shading Triangle Normal + Smooth Shading

What’s the difference?

Flat Shading VS. Smooth Shading

• Flat shading has this discontinuous artifact.• It is fast, since only needs one calculation per polygon.• Only useful when the polygons are very small.

• Smooth shading avoid the discontinuous artifact.• Slightly slower.• More realistic.

Smooth Shading• OpenGL uses a smooth Gouraud shading technique.• The basic idea is to calculate the color intensity at each

vertex, and then interpolate over the polygon.• To use smooth shading:

glShadeModel(GL_SMOOTH)

Vertex Normal + Flat Shading Vertex Normal + Smooth Shading

Review: Linear Interpolation

Vp

P

Q

Vq

R

Vr=?

• Given a line segment with two end points (P and Q) and a sample point R, we can interpolate a value function V over the line as:

Vr =Q−R V p+ P−R V θ

P−Q

OpenGL Interpolation• OpenGL does 2D interpolation in a scanline way.• The result is identical to the interpolation using barycentric

coordinates. But the scanline method is faster. Why?

For every scanline

Gouraud Shading• Gouraud shading calculates the color per vertex.• It has artifacts too.• To solve it, use smaller polygons.

dark

dark

dark

darkdark or bright?

Phong Shading• Instead of interpolating the color (light intensity), Phong shading

interpolates surface normals, and then calculates the 3D reflection per 2D pixel.

• OpenGL doesn’t support it, since 3D information needs to be carried through the whole pipeline.

• GPU supports it. You can use OpenGL shading language (GLSL).• It’s still under the projection+scanline framework, but its result is

comparable to ray tracing.

Flat Shading Gouraud Shading Phong Shading

Summary• The projection+scanline graphics pipeline is also called

rasterization-based rendering.• Examples: OpenGL, Pixar Renderman, GPU…• Fast, but difficult to handle global illumination• Widely used in games

• Alternatively, ray tracing is based on the inverse-projection+ray-intersection framework• Examples: POV-Ray, new Pixar Renderman, PBRT…• Slow, but handles global illumination• Used for offline rendering, such as movie effects